Nuprl Lemma : rmul-rdiv-cancel5

[a,b,c:ℝ].  ((b/a) (a/c)) (b/c) supposing a ≠ r0 ∧ c ≠ r0


Proof




Definitions occuring in Statement :  rdiv: (x/y) rneq: x ≠ y req: y rmul: b int-to-real: r(n) real: uimplies: supposing a uall: [x:A]. B[x] and: P ∧ Q natural_number: $n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a and: P ∧ Q false: False implies:  Q not: ¬A rat_term_to_real: rat_term_to_real(f;t) rtermDivide: num "/" denom rat_term_ind: rat_term_ind rtermVar: rtermVar(var) pi1: fst(t) true: True rtermMultiply: left "*" right pi2: snd(t) prop:
Lemmas referenced :  assert-rat-term-eq2 rtermMultiply_wf rtermDivide_wf rtermVar_wf int-to-real_wf istype-int req_witness rmul_wf rdiv_wf rneq_wf real_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut sqequalHypSubstitution productElimination thin extract_by_obid isectElimination natural_numberEquality hypothesis lambdaEquality_alt int_eqEquality hypothesisEquality independent_isectElimination approximateComputation sqequalRule independent_pairFormation independent_functionElimination productIsType universeIsType isect_memberEquality_alt because_Cache isectIsTypeImplies inhabitedIsType

Latex:
\mforall{}[a,b,c:\mBbbR{}].    ((b/a)  *  (a/c))  =  (b/c)  supposing  a  \mneq{}  r0  \mwedge{}  c  \mneq{}  r0



Date html generated: 2019_10_29-AM-09_55_12
Last ObjectModification: 2019_04_01-PM-07_05_36

Theory : reals


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